framework does not restrict you to the use of PHP, extensions or other libraries.
For request any API by REST you can use Guzzle / PSR-0 compatible library. I think that it is best choice for now.
https://packagist.org/packages/guzzle/guzzle

Phalcon doesn't have instruments for your task. You must use third party libs or php native functions. For example something like this https://github.com/slava-basko/MegaCurl/ it's wrapper for PHP Curl for comfortable work. I hope this will help you =)